Question
Asked Nov 27, 2019
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A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2 ft/s, how fast is the
angle between the top of the ladder and the wall changing when the angle is T/4 rad?
rad/s
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A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2 ft/s, how fast is the angle between the top of the ladder and the wall changing when the angle is T/4 rad? rad/s

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Expert Answer

Step 1

Let x be the distance between the base of the wall and the bottom of the ladder. And let θ be the angle between the top of the ladder and the wall.

Then:

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Base sin 0 Hypotenuse 10 x 10 sin Differentiate with respect to 't: dx =10(sin e) dt dt dx =10 cos e dt de dt

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Step 2

dx/dt = 2ft/s and we seek dθ/dt when θ = π/4:

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dx =10 cos e dt de dt de 2 10 cos dt 2 de 2 10 cos 4 2 dt 2 de 2 52 dt de 2 dt 52

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Step 3

Rationalization of ...

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de 2 dt 5/2 5/2 de 102 (52) de 102 dt dt 25x2 de 102 dt 50 dе 2 dt 5

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Tagged in

Math

Calculus

Derivative